Question

What are the intercepts of $y=4x-5$ ?

Answer 1

To solve this problem, we need to express it in the intercept form $\dfrac{x}{a}+\dfrac{y}{b}=1$ . Here, a is the x intercept and b is the y intercept. The given equation becomes $\dfrac{x}{\dfrac{5}{4}}-\dfrac{y}{5}=1$ . Comparing, we get, $a=\dfrac{5}{4},b=-5$ .

Complete step-by-step solution:
A straight line is a two-dimensional figure which can be defined as the locus of a point which travels such that either the sum or difference of the x and y coordinates remains the same or constant. A straight line extends from infinity to infinity.
In the cartesian coordinate system, there are different forms of a straight line. These forms are the slope-intercept form, the intercept form and so on. The slope intercept form is of the form $y=mx+c$ . Here, m is the slope and c is the y-intercept. The intercept form is of the form $\dfrac{x}{a}+\dfrac{y}{b}=1$ . Here, a is the x intercept and b is the y intercept.
In order to find the x and y intercepts of the given line, we need to arrange it in the intercept form. At first, we bring y to the RHS and $5$ to the LHS. This gives,
$\Rightarrow 4x-y=5$
We then divide the two sides of the equation by $5$ . This gives,
$\Rightarrow \dfrac{4}{5}x-\dfrac{1}{5}y=1$
Rearranging, we get,
$\Rightarrow \dfrac{x}{\dfrac{5}{4}}-\dfrac{y}{5}=1$
Thus, we can conclude that the x intercept is $\dfrac{5}{4}$ and the y intercept is $-5$ .

Note: We can also solve the problem in another way. In order to find the x intercept, we will put $y=0$ in the given equation and get,
$\begin{aligned} & 0=4x-5 \\\ & \Rightarrow x=\dfrac{5}{4} \\\ \end{aligned}$
To get the y intercept, we put $x=0$ to get,
$\begin{aligned} & y=0-5 \\\ & \Rightarrow y=-5 \\\ \end{aligned}$